| | step type | requirements | statement |
| 0 | modus ponens | 1, 2 | ⊢  |
| 1 | instantiation | 3, 4*, 5*, 6* | ⊢  |
| | : , : , :  |
| 2 | instantiation | 7, 8, 9 | ⊢  |
| | : , :  |
| 3 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.fold_forall_natural_pos |
| 4 | instantiation | 601, 10, 449 | ⊢  |
| | : , : , :  |
| 5 | instantiation | 11, 12 | ⊢  |
| | :  |
| 6 | instantiation | 601, 13, 14 | ⊢  |
| | : , : , :  |
| 7 | theorem | | ⊢  |
| | proveit.logic.booleans.conjunction.and_if_both |
| 8 | instantiation | 427, 15, 16 | ⊢  |
| | : , : , :  |
| 9 | generalization | 17 | ⊢  |
| 10 | instantiation | 615, 630 | ⊢  |
| | : , : , :  |
| 11 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.single_qubit_num_ket |
| 12 | instantiation | 18, 19, 20 | ⊢  |
| | :  |
| 13 | instantiation | 615, 126 | ⊢  |
| | : , : , :  |
| 14 | instantiation | 460, 21 | ⊢  |
| | : , :  |
| 15 | instantiation | 102, 679, 22, 23* | ⊢  |
| | :  |
| 16 | instantiation | 615, 24 | ⊢  |
| | : , : , :  |
| 17 | instantiation | 460, 25 | , ⊢  |
| | : , :  |
| 18 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nonneg_int_is_natural |
| 19 | instantiation | 682, 26, 28 | ⊢  |
| | : , : , :  |
| 20 | instantiation | 27, 636, 663, 28 | ⊢  |
| | : , : , :  |
| 21 | instantiation | 29, 644, 679, 671, 630* | ⊢  |
| | : , : , :  |
| 22 | instantiation | 543, 30, 31 | ⊢  |
| | : , : , :  |
| 23 | instantiation | 601, 32, 33 | ⊢  |
| | : , : , :  |
| 24 | instantiation | 34, 636, 663, 35, 36*, 37* | ⊢  |
| | : , : , : , :  |
| 25 | instantiation | 543, 38, 39 | , ⊢  |
| | : , : , :  |
| 26 | instantiation | 635, 636, 663 | ⊢  |
| | : , :  |
| 27 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.interval_lower_bound |
| 28 | assumption | | ⊢  |
| 29 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.product_of_posnat_powers |
| 30 | instantiation | 477, 344, 613, 299 | ⊢  |
| | : , : , :  |
| 31 | instantiation | 492, 613, 575 | ⊢  |
| | : , :  |
| 32 | instantiation | 615, 40 | ⊢  |
| | : , : , :  |
| 33 | instantiation | 41, 485, 42 | ⊢  |
| | : , : , :  |
| 34 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.vec_sum_split_first |
| 35 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.less_0_1 |
| 36 | instantiation | 601, 43, 44 | ⊢  |
| | : , : , :  |
| 37 | instantiation | 601, 45, 46 | ⊢  |
| | : , : , :  |
| 38 | instantiation | 543, 47, 48, 49* | , ⊢  |
| | : , : , :  |
| 39 | instantiation | 601, 50, 51 | ⊢  |
| | : , : , :  |
| 40 | instantiation | 52, 679, 53 | ⊢  |
| | : , : , :  |
| 41 | axiom | | ⊢  |
| | proveit.linear_algebra.tensors.unary_tensor_prod_def |
| 42 | instantiation | 453, 485, 203, 54 | ⊢  |
| | : , : , : , :  |
| 43 | instantiation | 615, 55 | ⊢  |
| | : , : , :  |
| 44 | instantiation | 56, 613, 325, 485 | ⊢  |
| | : , : , :  |
| 45 | instantiation | 615, 57 | ⊢  |
| | : , : , :  |
| 46 | instantiation | 58, 663, 59* | ⊢  |
| | : , :  |
| 47 | instantiation | 427, 60, 61 | , ⊢  |
| | : , : , :  |
| 48 | instantiation | 102, 671 | ⊢  |
| | :  |
| 49 | instantiation | 601, 62, 63 | ⊢  |
| | : , : , :  |
| 50 | instantiation | 460, 64 | ⊢  |
| | : , :  |
| 51 | instantiation | 460, 65 | ⊢  |
| | : , :  |
| 52 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_eq_via_elem_eq |
| 53 | instantiation | 615, 66 | ⊢  |
| | : , : , :  |
| 54 | instantiation | 324, 485, 325, 67 | ⊢  |
| | : , : , : , :  |
| 55 | instantiation | 601, 68, 69 | ⊢  |
| | : , : , :  |
| 56 | conjecture | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.one_as_scalar_mult_id |
| 57 | modus ponens | 70, 71 | ⊢  |
| 58 | axiom | | ⊢  |
| | proveit.linear_algebra.addition.vec_sum_single |
| 59 | instantiation | 591, 421, 610, 422, 612, 644, 567, 580, 581 | ⊢  |
| | : , : , : , :  |
| 60 | instantiation | 543, 72, 73 | ⊢  |
| | : , : , :  |
| 61 | assumption | | ⊢  |
| 62 | instantiation | 74, 672, 194, 610, 164, 106, 612, 485, 107, 108, 75, 110 | ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 63 | instantiation | 456, 281, 610, 194, 612, 164, 106, 485, 107, 108, 278, 110 | ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 64 | instantiation | 76, 684, 77, 78, 79, 80 | ⊢  |
| | : , : , : , :  |
| 65 | instantiation | 81, 158, 82, 83, 84, 85, 86* | ⊢  |
| | : , : , : , :  |
| 66 | instantiation | 615, 87 | ⊢  |
| | : , : , :  |
| 67 | instantiation | 453, 485, 88, 488 | ⊢  |
| | : , : , : , :  |
| 68 | instantiation | 615, 89 | ⊢  |
| | : , : , :  |
| 69 | instantiation | 302, 490 | ⊢  |
| | :  |
| 70 | instantiation | 90, 679 | ⊢  |
| | : , : , : , : , : , :  |
| 71 | generalization | 91 | ⊢  |
| 72 | instantiation | 92, 93 | ⊢  |
| | : , : , :  |
| 73 | instantiation | 601, 94, 95 | ⊢  |
| | : , : , :  |
| 74 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_disassociation |
| 75 | instantiation | 453, 485, 281, 278 | ⊢  |
| | : , : , : , :  |
| 76 | axiom | | ⊢  |
| | proveit.core_expr_types.operations.operands_substitution |
| 77 | instantiation | 624 | ⊢  |
| | : , :  |
| 78 | instantiation | 624 | ⊢  |
| | : , :  |
| 79 | instantiation | 460, 437 | ⊢  |
| | : , :  |
| 80 | instantiation | 615, 96 | ⊢  |
| | : , : , :  |
| 81 | conjecture | | ⊢  |
| | proveit.logic.equality.sub_in_right_operands_via_tuple |
| 82 | instantiation | 283, 97, 98, 101 | ⊢  |
| | : , : , : , :  |
| 83 | instantiation | 283, 99, 100, 101 | ⊢  |
| | : , : , : , :  |
| 84 | instantiation | 102, 638, 103 | ⊢  |
| | :  |
| 85 | instantiation | 104, 105, 292* | ⊢  |
| | : , : , :  |
| 86 | instantiation | 456, 203, 610, 194, 612, 164, 106, 485, 107, 108, 109, 110 | ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 87 | instantiation | 615, 111 | ⊢  |
| | : , : , :  |
| 88 | instantiation | 540, 490, 112 | ⊢  |
| | : , :  |
| 89 | instantiation | 113, 421, 610, 422, 612, 644, 567, 580, 581 | ⊢  |
| | : , : , : , :  |
| 90 | axiom | | ⊢  |
| | proveit.core_expr_types.lambda_maps.lambda_substitution |
| 91 | instantiation | 615, 114 | ⊢  |
| | : , : , :  |
| 92 | theorem | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.scalar_mult_eq |
| 93 | instantiation | 142, 115, 116 | ⊢  |
| | : , :  |
| 94 | instantiation | 615, 117 | ⊢  |
| | : , : , :  |
| 95 | instantiation | 460, 118 | ⊢  |
| | : , :  |
| 96 | instantiation | 460, 135 | ⊢  |
| | : , :  |
| 97 | instantiation | 543, 119, 120 | ⊢  |
| | : , : , :  |
| 98 | instantiation | 572 | ⊢  |
| | :  |
| 99 | instantiation | 121, 681, 122, 123, 124, 125, 194, 157*, 164* | ⊢  |
| | : , : , : , :  |
| 100 | instantiation | 460, 126 | ⊢  |
| | : , :  |
| 101 | instantiation | 460, 127 | ⊢  |
| | : , :  |
| 102 | axiom | | ⊢  |
| | proveit.physics.quantum.QPE._psi_t_def |
| 103 | instantiation | 601, 128, 129 | ⊢  |
| | : , : , :  |
| 104 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.partition_front |
| 105 | instantiation | 130, 610, 191 | ⊢  |
| | : , :  |
| 106 | instantiation | 283, 131, 410, 134 | ⊢  |
| | : , : , : , :  |
| 107 | instantiation | 132, 620, 636, 485, 168 | ⊢  |
| | : , : , :  |
| 108 | instantiation | 283, 133, 410, 134 | ⊢  |
| | : , : , : , :  |
| 109 | instantiation | 543, 278, 135 | ⊢  |
| | : , : , :  |
| 110 | modus ponens | 136, 137 | ⊢  |
| 111 | instantiation | 615, 138 | ⊢  |
| | : , : , :  |
| 112 | instantiation | 543, 139, 140 | ⊢  |
| | : , : , :  |
| 113 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_zero_any |
| 114 | instantiation | 615, 141 | ⊢  |
| | : , : , :  |
| 115 | instantiation | 142, 143, 144 | ⊢  |
| | : , :  |
| 116 | instantiation | 615, 145, 146*, 147*, 148* | ⊢  |
| | : , : , :  |
| 117 | instantiation | 601, 149, 150 | ⊢  |
| | : , : , :  |
| 118 | instantiation | 283, 151, 152, 153 | ⊢  |
| | : , : , : , :  |
| 119 | instantiation | 193, 154 | ⊢  |
| | : , : , :  |
| 120 | instantiation | 601, 155, 156 | ⊢  |
| | : , : , :  |
| 121 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.general_len |
| 122 | instantiation | 624 | ⊢  |
| | : , :  |
| 123 | instantiation | 624 | ⊢  |
| | : , :  |
| 124 | instantiation | 624 | ⊢  |
| | : , :  |
| 125 | instantiation | 427, 672, 157 | ⊢  |
| | : , : , :  |
| 126 | instantiation | 492, 618, 613 | ⊢  |
| | : , :  |
| 127 | instantiation | 197, 158 | ⊢  |
| | : , :  |
| 128 | instantiation | 615, 159 | ⊢  |
| | : , : , :  |
| 129 | instantiation | 601, 160, 161 | ⊢  |
| | : , : , :  |
| 130 | conjecture | | ⊢  |
| | proveit.numbers.addition.add_nat_closure_bin |
| 131 | instantiation | 543, 162, 164 | ⊢  |
| | : , : , :  |
| 132 | conjecture | | ⊢  |
| | proveit.logic.booleans.conjunction.redundant_conjunction_general |
| 133 | instantiation | 543, 163, 164 | ⊢  |
| | : , : , :  |
| 134 | instantiation | 460, 165 | ⊢  |
| | : , :  |
| 135 | instantiation | 615, 166 | ⊢  |
| | : , : , :  |
| 136 | instantiation | 167, 620, 636, 168 | ⊢  |
| | : , : , : , :  |
| 137 | generalization | 169 | ⊢  |
| 138 | instantiation | 601, 170, 171 | ⊢  |
| | : , : , :  |
| 139 | instantiation | 579, 546, 564 | ⊢  |
| | : , :  |
| 140 | instantiation | 601, 172, 173 | ⊢  |
| | : , : , :  |
| 141 | instantiation | 615, 299 | ⊢  |
| | : , : , :  |
| 142 | theorem | | ⊢  |
| | proveit.logic.equality.rhs_via_equality |
| 143 | instantiation | 543, 174, 175 | ⊢  |
| | : , : , :  |
| 144 | instantiation | 615, 176, 177*, 178*, 179* | ⊢  |
| | : , : , :  |
| 145 | modus ponens | 180, 181 | ⊢  |
| 146 | instantiation | 318, 622 | ⊢  |
| | : , :  |
| 147 | instantiation | 318, 622 | ⊢  |
| | : , :  |
| 148 | instantiation | 460, 182 | ⊢  |
| | : , :  |
| 149 | instantiation | 615, 183 | ⊢  |
| | : , : , :  |
| 150 | modus ponens | 184, 185 | ⊢  |
| 151 | instantiation | 601, 186, 187, 188* | ⊢  |
| | : , : , :  |
| 152 | instantiation | 615, 189 | ⊢  |
| | : , : , :  |
| 153 | instantiation | 572 | ⊢  |
| | :  |
| 154 | instantiation | 235, 547, 190, 610, 191, 672 | ⊢  |
| | : , :  |
| 155 | instantiation | 615, 292 | ⊢  |
| | : , : , :  |
| 156 | instantiation | 345, 610, 684, 612, 611, 618, 613 | ⊢  |
| | : , : , : , :  |
| 157 | instantiation | 341, 613, 310 | ⊢  |
| | : , : , :  |
| 158 | instantiation | 682, 670, 638 | ⊢  |
| | : , : , :  |
| 159 | instantiation | 291, 618, 613 | ⊢  |
| | : , :  |
| 160 | instantiation | 552, 610, 684, 672, 612, 192, 408, 575, 613 | ⊢  |
| | : , : , : , : , : , :  |
| 161 | instantiation | 309, 613, 408, 310 | ⊢  |
| | : , : , :  |
| 162 | instantiation | 193, 194 | ⊢  |
| | : , : , :  |
| 163 | instantiation | 193, 194 | ⊢  |
| | : , : , :  |
| 164 | instantiation | 601, 195, 196 | ⊢  |
| | : , : , :  |
| 165 | instantiation | 197, 661 | ⊢  |
| | : , :  |
| 166 | instantiation | 615, 198 | ⊢  |
| | : , : , :  |
| 167 | conjecture | | ⊢  |
| | proveit.logic.booleans.conjunction.conjunction_from_quantification |
| 168 | instantiation | 374, 199, 257, 631, 200, 201*, 202* | ⊢  |
| | : , : , :  |
| 169 | instantiation | 453, 485, 203, 204 | , ⊢  |
| | : , : , : , :  |
| 170 | instantiation | 615, 205 | ⊢  |
| | : , : , :  |
| 171 | instantiation | 591, 547, 672, 296, 644, 567, 580, 581 | ⊢  |
| | : , : , : , :  |
| 172 | instantiation | 574, 672, 684, 610, 565, 612, 546, 580, 581 | ⊢  |
| | : , : , : , : , : , :  |
| 173 | instantiation | 574, 610, 684, 612, 548, 565, 644, 567, 580, 581 | ⊢  |
| | : , : , : , : , : , :  |
| 174 | instantiation | 206, 636, 637, 211, 207, 208, 209* | ⊢  |
| | : , : , : , : , :  |
| 175 | instantiation | 210, 649, 211, 446, 212*, 213*, 214* | ⊢  |
| | : , : , : , : , :  |
| 176 | modus ponens | 215, 216 | ⊢  |
| 177 | instantiation | 318, 622 | ⊢  |
| | : , :  |
| 178 | instantiation | 318, 622 | ⊢  |
| | : , :  |
| 179 | instantiation | 283, 217, 218, 219 | ⊢  |
| | : , : , : , :  |
| 180 | instantiation | 359, 679 | ⊢  |
| | : , : , : , : , : , : , :  |
| 181 | generalization | 220 | ⊢  |
| 182 | modus ponens | 221, 222 | ⊢  |
| 183 | instantiation | 460, 223 | ⊢  |
| | : , :  |
| 184 | instantiation | 224, 610, 684, 672, 225, 612, 226 | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 185 | instantiation | 645, 227, 231 | ⊢  |
| | : , : , :  |
| 186 | instantiation | 456, 281, 610, 672, 612, 485, 486, 278, 228 | ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 187 | instantiation | 615, 229 | ⊢  |
| | : , : , :  |
| 188 | instantiation | 230, 454, 231, 281, 282, 232* | ⊢  |
| | : , : , : , : , :  |
| 189 | instantiation | 460, 233 | ⊢  |
| | : , :  |
| 190 | instantiation | 568 | ⊢  |
| | : , : , :  |
| 191 | instantiation | 682, 670, 234 | ⊢  |
| | : , : , :  |
| 192 | instantiation | 624 | ⊢  |
| | : , :  |
| 193 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.range_len |
| 194 | instantiation | 235, 547, 236, 610, 237, 672 | ⊢  |
| | : , :  |
| 195 | instantiation | 615, 238 | ⊢  |
| | : , : , :  |
| 196 | instantiation | 283, 239, 240, 241 | ⊢  |
| | : , : , : , :  |
| 197 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.range_from1_len |
| 198 | instantiation | 615, 242 | ⊢  |
| | : , : , :  |
| 199 | instantiation | 682, 668, 243 | ⊢  |
| | : , : , :  |
| 200 | instantiation | 244, 245 | ⊢  |
| | : , :  |
| 201 | instantiation | 601, 246, 247 | ⊢  |
| | : , : , :  |
| 202 | instantiation | 283, 248, 310, 249 | ⊢  |
| | : , : , : , :  |
| 203 | instantiation | 458, 613, 465, 466 | ⊢  |
| | : , :  |
| 204 | instantiation | 324, 485, 325, 250 | , ⊢  |
| | : , : , : , :  |
| 205 | instantiation | 601, 251, 252 | ⊢  |
| | : , : , :  |
| 206 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.vec_sum_split_after |
| 207 | instantiation | 253, 254 | ⊢  |
| | : , :  |
| 208 | instantiation | 255, 256, 257, 542, 258, 259*, 260* | ⊢  |
| | : , : , :  |
| 209 | instantiation | 601, 261, 262 | ⊢  |
| | : , : , :  |
| 210 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.vec_sum_index_shift |
| 211 | instantiation | 648, 445, 650 | ⊢  |
| | : , :  |
| 212 | instantiation | 409, 525, 263 | ⊢  |
| | : , :  |
| 213 | instantiation | 601, 264, 265 | ⊢  |
| | : , : , :  |
| 214 | instantiation | 339, 525 | ⊢  |
| | :  |
| 215 | instantiation | 359, 679 | ⊢  |
| | : , : , : , : , : , : , :  |
| 216 | generalization | 266 | ⊢  |
| 217 | instantiation | 615, 267, 268*, 269* | ⊢  |
| | : , : , :  |
| 218 | instantiation | 460, 270 | ⊢  |
| | : , :  |
| 219 | instantiation | 615, 271 | ⊢  |
| | : , : , :  |
| 220 | instantiation | 272, 671, 622 | , ⊢  |
| | : , :  |
| 221 | instantiation | 392, 672, 679, 610, 454, 612 | ⊢  |
| | : , : , : , : , : , : , : , : , : , : , :  |
| 222 | generalization | 273 | ⊢  |
| 223 | instantiation | 456, 390, 610, 672, 612, 485, 486, 488, 279 | ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 224 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_factorization_from_add |
| 225 | instantiation | 509, 274 | ⊢  |
| | :  |
| 226 | instantiation | 624 | ⊢  |
| | : , :  |
| 227 | instantiation | 275, 681, 276, 510 | ⊢  |
| | : , : , :  |
| 228 | instantiation | 453, 486, 282, 279 | ⊢  |
| | : , : , : , :  |
| 229 | instantiation | 456, 282, 672, 610, 612, 485, 486, 278, 279 | ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 230 | conjecture | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled |
| 231 | instantiation | 483, 681, 484, 485, 486, 277, 278, 279 | ⊢  |
| | : , : , : , :  |
| 232 | instantiation | 280, 281, 282 | ⊢  |
| | : , :  |
| 233 | instantiation | 283, 284, 285, 286 | ⊢  |
| | : , : , : , :  |
| 234 | instantiation | 287, 288 | ⊢  |
| | :  |
| 235 | conjecture | | ⊢  |
| | proveit.numbers.addition.add_nat_closure |
| 236 | instantiation | 568 | ⊢  |
| | : , : , :  |
| 237 | instantiation | 289, 290 | ⊢  |
| | :  |
| 238 | instantiation | 291, 408, 613, 292* | ⊢  |
| | : , :  |
| 239 | instantiation | 552, 672, 684, 293, 344, 618, 575, 613 | ⊢  |
| | : , : , : , : , : , :  |
| 240 | instantiation | 345, 610, 547, 612, 294, 618, 575, 613 | ⊢  |
| | : , : , : , :  |
| 241 | instantiation | 309, 613, 618, 310 | ⊢  |
| | : , : , :  |
| 242 | instantiation | 295, 547, 672, 610, 296, 612, 644, 567, 580, 581, 525 | ⊢  |
| | : , : , : , : , : , : , :  |
| 243 | instantiation | 682, 677, 620 | ⊢  |
| | : , : , :  |
| 244 | conjecture | | ⊢  |
| | proveit.numbers.ordering.relax_less |
| 245 | instantiation | 304, 671 | ⊢  |
| | :  |
| 246 | instantiation | 552, 672, 684, 610, 340, 612, 344, 408, 613 | ⊢  |
| | : , : , : , : , : , :  |
| 247 | instantiation | 345, 610, 684, 612, 340, 408, 613 | ⊢  |
| | : , : , : , :  |
| 248 | instantiation | 601, 297, 298 | ⊢  |
| | : , : , :  |
| 249 | instantiation | 460, 299 | ⊢  |
| | : , :  |
| 250 | instantiation | 453, 485, 300, 488 | , ⊢  |
| | : , : , : , :  |
| 251 | instantiation | 615, 301 | ⊢  |
| | : , : , :  |
| 252 | instantiation | 302, 644 | ⊢  |
| | :  |
| 253 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.nonneg_difference |
| 254 | instantiation | 407, 510 | ⊢  |
| | :  |
| 255 | conjecture | | ⊢  |
| | proveit.numbers.addition.strong_bound_via_left_term_bound |
| 256 | instantiation | 682, 668, 303 | ⊢  |
| | : , : , :  |
| 257 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.zero_is_real |
| 258 | instantiation | 304, 510 | ⊢  |
| | :  |
| 259 | instantiation | 601, 305, 306 | ⊢  |
| | : , : , :  |
| 260 | instantiation | 601, 307, 308 | ⊢  |
| | : , : , :  |
| 261 | instantiation | 552, 610, 684, 672, 612, 346, 525, 575, 613 | ⊢  |
| | : , : , : , : , : , :  |
| 262 | instantiation | 309, 613, 525, 310 | ⊢  |
| | : , : , :  |
| 263 | instantiation | 572 | ⊢  |
| | :  |
| 264 | instantiation | 552, 610, 684, 672, 612, 311, 352, 575, 353 | ⊢  |
| | : , : , : , : , : , :  |
| 265 | instantiation | 601, 312, 313 | ⊢  |
| | : , : , :  |
| 266 | instantiation | 543, 314, 315 | , ⊢  |
| | : , : , :  |
| 267 | modus ponens | 316, 317 | ⊢  |
| 268 | instantiation | 318, 622 | ⊢  |
| | : , :  |
| 269 | instantiation | 318, 622 | ⊢  |
| | : , :  |
| 270 | modus ponens | 319, 320 | ⊢  |
| 271 | instantiation | 460, 321 | ⊢  |
| | : , :  |
| 272 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.prepend_num_ket_with_zero_ket |
| 273 | instantiation | 483, 681, 484, 485, 486, 322, 325, 366 | , ⊢  |
| | : , : , : , :  |
| 274 | instantiation | 323, 681, 510 | ⊢  |
| | : , :  |
| 275 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp |
| 276 | instantiation | 624 | ⊢  |
| | : , :  |
| 277 | instantiation | 624 | ⊢  |
| | : , :  |
| 278 | instantiation | 324, 485, 325, 326 | ⊢  |
| | : , : , : , :  |
| 279 | modus ponens | 327, 328 | ⊢  |
| 280 | axiom | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult |
| 281 | instantiation | 458, 613, 329, 330 | ⊢  |
| | : , :  |
| 282 | instantiation | 458, 613, 331, 332 | ⊢  |
| | : , :  |
| 283 | conjecture | | ⊢  |
| | proveit.logic.equality.four_chain_transitivity |
| 284 | instantiation | 601, 333, 334 | ⊢  |
| | : , : , :  |
| 285 | instantiation | 572 | ⊢  |
| | :  |
| 286 | instantiation | 460, 335 | ⊢  |
| | : , :  |
| 287 | conjecture | | ⊢  |
| | proveit.numbers.negation.nat_pos_closure |
| 288 | instantiation | 336, 671 | ⊢  |
| | :  |
| 289 | conjecture | | ⊢  |
| | proveit.numbers.negation.nat_closure |
| 290 | instantiation | 337, 620, 338 | ⊢  |
| | :  |
| 291 | conjecture | | ⊢  |
| | proveit.numbers.negation.distribute_neg_through_binary_sum |
| 292 | instantiation | 339, 618 | ⊢  |
| | :  |
| 293 | instantiation | 624 | ⊢  |
| | : , :  |
| 294 | instantiation | 568 | ⊢  |
| | : , : , :  |
| 295 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.leftward_commutation |
| 296 | instantiation | 568 | ⊢  |
| | : , : , :  |
| 297 | instantiation | 552, 672, 684, 610, 340, 612, 618, 408, 613 | ⊢  |
| | : , : , : , : , : , :  |
| 298 | instantiation | 341, 618, 613, 410 | ⊢  |
| | : , : , :  |
| 299 | instantiation | 342, 613 | ⊢  |
| | :  |
| 300 | instantiation | 540, 490, 343 | , ⊢  |
| | : , :  |
| 301 | conjecture | | ⊢  |
| | proveit.numbers.negation.negated_zero |
| 302 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_zero_eq_one |
| 303 | instantiation | 682, 677, 637 | ⊢  |
| | : , : , :  |
| 304 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos |
| 305 | instantiation | 552, 672, 684, 610, 346, 612, 344, 525, 575 | ⊢  |
| | : , : , : , : , : , :  |
| 306 | instantiation | 345, 610, 684, 612, 346, 525, 575 | ⊢  |
| | : , : , : , :  |
| 307 | instantiation | 552, 672, 684, 610, 346, 612, 525, 575 | ⊢  |
| | : , : , : , : , : , :  |
| 308 | instantiation | 350, 610, 684, 672, 612, 347, 525, 575, 348* | ⊢  |
| | : , : , : , : , : , :  |
| 309 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_triple_32 |
| 310 | instantiation | 572 | ⊢  |
| | :  |
| 311 | instantiation | 624 | ⊢  |
| | : , :  |
| 312 | instantiation | 349, 672, 610, 612, 352, 575, 353 | ⊢  |
| | : , : , : , : , : , : , :  |
| 313 | instantiation | 350, 610, 684, 672, 612, 351, 352, 353, 575, 354* | ⊢  |
| | : , : , : , : , : , :  |
| 314 | instantiation | 427, 355, 356 | , ⊢  |
| | : , : , :  |
| 315 | instantiation | 601, 357, 358 | , ⊢  |
| | : , : , :  |
| 316 | instantiation | 359, 679 | ⊢  |
| | : , : , : , : , : , : , :  |
| 317 | generalization | 360 | ⊢  |
| 318 | conjecture | | ⊢  |
| | proveit.core_expr_types.conditionals.satisfied_condition_reduction |
| 319 | instantiation | 361, 679, 454, 390 | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 320 | modus ponens | 362, 363 | ⊢  |
| 321 | modus ponens | 364, 365 | ⊢  |
| 322 | instantiation | 624 | ⊢  |
| | : , :  |
| 323 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_nat_pos_closure_bin |
| 324 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.binary_closure |
| 325 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.ket_zero_in_qubit_space |
| 326 | instantiation | 453, 485, 390, 488 | ⊢  |
| | : , : , : , :  |
| 327 | instantiation | 391, 679, 486 | ⊢  |
| | : , : , : , : , : , :  |
| 328 | generalization | 366 | ⊢  |
| 329 | instantiation | 540, 644, 367 | ⊢  |
| | : , :  |
| 330 | instantiation | 427, 466, 464 | ⊢  |
| | : , : , :  |
| 331 | instantiation | 540, 644, 430 | ⊢  |
| | : , :  |
| 332 | instantiation | 427, 470, 468 | ⊢  |
| | : , : , :  |
| 333 | instantiation | 615, 368 | ⊢  |
| | : , : , :  |
| 334 | instantiation | 586, 613, 369, 370, 371* | ⊢  |
| | : , :  |
| 335 | instantiation | 601, 372, 373 | ⊢  |
| | : , : , :  |
| 336 | conjecture | | ⊢  |
| | proveit.numbers.negation.int_neg_closure |
| 337 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
| 338 | instantiation | 374, 441, 625, 631, 375, 376*, 377* | ⊢  |
| | : , : , :  |
| 339 | conjecture | | ⊢  |
| | proveit.numbers.negation.double_negation |
| 340 | instantiation | 624 | ⊢  |
| | : , :  |
| 341 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_triple_12 |
| 342 | conjecture | | ⊢  |
| | proveit.numbers.addition.elim_zero_left |
| 343 | instantiation | 543, 378, 379 | , ⊢  |
| | : , : , :  |
| 344 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.zero_is_complex |
| 345 | conjecture | | ⊢  |
| | proveit.numbers.addition.elim_zero_any |
| 346 | instantiation | 624 | ⊢  |
| | : , :  |
| 347 | instantiation | 624 | ⊢  |
| | : , :  |
| 348 | instantiation | 460, 380, 478* | ⊢  |
| | : , :  |
| 349 | conjecture | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 350 | conjecture | | ⊢  |
| | proveit.numbers.addition.association |
| 351 | instantiation | 624 | ⊢  |
| | : , :  |
| 352 | instantiation | 682, 655, 381 | ⊢  |
| | : , : , :  |
| 353 | instantiation | 682, 655, 382 | ⊢  |
| | : , : , :  |
| 354 | instantiation | 601, 383, 384, 385* | ⊢  |
| | : , : , :  |
| 355 | instantiation | 615, 386 | , ⊢  |
| | : , : , :  |
| 356 | instantiation | 387, 527, 491, 426 | , ⊢  |
| | : , : , :  |
| 357 | instantiation | 460, 388 | , ⊢  |
| | : , :  |
| 358 | instantiation | 389, 671, 622 | , ⊢  |
| | : , :  |
| 359 | conjecture | | ⊢  |
| | proveit.core_expr_types.lambda_maps.general_lambda_substitution |
| 360 | instantiation | 617, 457, 390 | , ⊢  |
| | : , :  |
| 361 | conjecture | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult |
| 362 | instantiation | 391, 679, 454 | ⊢  |
| | : , : , : , : , : , :  |
| 363 | generalization | 428 | ⊢  |
| 364 | instantiation | 392, 672, 679, 610, 454, 612 | ⊢  |
| | : , : , : , : , : , : , : , : , : , : , :  |
| 365 | generalization | 393 | ⊢  |
| 366 | instantiation | 453, 486, 457, 489 | , ⊢  |
| | : , : , : , :  |
| 367 | instantiation | 394, 395, 396 | ⊢  |
| | : , :  |
| 368 | instantiation | 601, 397, 398 | ⊢  |
| | : , : , :  |
| 369 | instantiation | 579, 465, 469 | ⊢  |
| | : , :  |
| 370 | instantiation | 399, 684, 400, 401, 402 | ⊢  |
| | : , :  |
| 371 | instantiation | 601, 403, 404 | ⊢  |
| | : , : , :  |
| 372 | instantiation | 615, 405 | ⊢  |
| | : , : , :  |
| 373 | instantiation | 615, 406 | ⊢  |
| | : , : , :  |
| 374 | conjecture | | ⊢  |
| | proveit.numbers.addition.weak_bound_via_left_term_bound |
| 375 | instantiation | 407, 671 | ⊢  |
| | :  |
| 376 | instantiation | 492, 613, 408 | ⊢  |
| | : , :  |
| 377 | instantiation | 409, 618, 410 | ⊢  |
| | : , :  |
| 378 | instantiation | 579, 546, 411 | , ⊢  |
| | : , :  |
| 379 | instantiation | 601, 412, 413 | , ⊢  |
| | : , : , :  |
| 380 | instantiation | 609, 610, 684, 672, 612, 414, 613, 525, 420* | ⊢  |
| | : , : , : , : , : , :  |
| 381 | instantiation | 682, 668, 415 | ⊢  |
| | : , : , :  |
| 382 | instantiation | 682, 668, 416 | ⊢  |
| | : , : , :  |
| 383 | instantiation | 615, 417 | ⊢  |
| | : , : , :  |
| 384 | instantiation | 460, 418 | ⊢  |
| | : , :  |
| 385 | instantiation | 601, 419, 420 | ⊢  |
| | : , : , :  |
| 386 | instantiation | 609, 421, 684, 610, 422, 423, 612, 644, 567, 580, 581, 566, 525 | , ⊢  |
| | : , : , : , : , : , :  |
| 387 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.product_of_complex_powers |
| 388 | instantiation | 424, 425 | , ⊢  |
| | : , : , :  |
| 389 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.prepend_num_ket_with_one_ket |
| 390 | instantiation | 540, 490, 426 | ⊢  |
| | : , :  |
| 391 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.summation_closure |
| 392 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult |
| 393 | instantiation | 427, 428, 429 | , ⊢  |
| | : , : , :  |
| 394 | conjecture | | ⊢  |
| | proveit.numbers.addition.add_complex_closure_bin |
| 395 | instantiation | 458, 608, 644, 587 | ⊢  |
| | : , :  |
| 396 | instantiation | 590, 430 | ⊢  |
| | :  |
| 397 | instantiation | 615, 550 | ⊢  |
| | : , : , :  |
| 398 | instantiation | 601, 431, 432 | ⊢  |
| | : , : , :  |
| 399 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_not_eq_zero |
| 400 | instantiation | 624 | ⊢  |
| | : , :  |
| 401 | instantiation | 433, 465, 466 | ⊢  |
| | :  |
| 402 | instantiation | 433, 469, 470 | ⊢  |
| | :  |
| 403 | instantiation | 615, 434 | ⊢  |
| | : , : , :  |
| 404 | instantiation | 601, 435, 436 | ⊢  |
| | : , : , :  |
| 405 | instantiation | 601, 437, 438 | ⊢  |
| | : , : , :  |
| 406 | instantiation | 601, 439, 440 | ⊢  |
| | : , : , :  |
| 407 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
| 408 | instantiation | 682, 655, 441 | ⊢  |
| | : , : , :  |
| 409 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_basic |
| 410 | instantiation | 572 | ⊢  |
| | :  |
| 411 | instantiation | 543, 442, 443 | , ⊢  |
| | : , : , :  |
| 412 | instantiation | 574, 672, 547, 610, 444, 612, 546, 580, 505, 581 | , ⊢  |
| | : , : , : , : , : , :  |
| 413 | instantiation | 574, 610, 684, 547, 612, 548, 444, 644, 567, 580, 505, 581 | , ⊢  |
| | : , : , : , : , : , :  |
| 414 | instantiation | 624 | ⊢  |
| | : , :  |
| 415 | instantiation | 682, 677, 445 | ⊢  |
| | : , : , :  |
| 416 | instantiation | 682, 677, 446 | ⊢  |
| | : , : , :  |
| 417 | instantiation | 460, 447 | ⊢  |
| | : , :  |
| 418 | instantiation | 609, 610, 684, 672, 612, 448, 644, 575, 525 | ⊢  |
| | : , : , : , : , : , :  |
| 419 | instantiation | 615, 449 | ⊢  |
| | : , : , :  |
| 420 | instantiation | 522, 525 | ⊢  |
| | :  |
| 421 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 422 | instantiation | 450 | ⊢  |
| | : , : , : , :  |
| 423 | instantiation | 624 | ⊢  |
| | : , :  |
| 424 | theorem | | ⊢  |
| | proveit.physics.quantum.algebra.num_ket_eq |
| 425 | instantiation | 492, 525, 566 | , ⊢  |
| | : , :  |
| 426 | instantiation | 543, 451, 452 | ⊢  |
| | : , : , :  |
| 427 | theorem | | ⊢  |
| | proveit.logic.equality.sub_left_side_into |
| 428 | instantiation | 453, 454, 457, 455 | , ⊢  |
| | : , : , : , :  |
| 429 | instantiation | 456, 457, 672, 610, 612, 485, 486, 488, 489 | , ⊢  |
| | : , : , : , : , : , : , : , : , : , :  |
| 430 | instantiation | 458, 618, 644, 587 | ⊢  |
| | : , :  |
| 431 | instantiation | 615, 459 | ⊢  |
| | : , : , :  |
| 432 | instantiation | 460, 461 | ⊢  |
| | : , :  |
| 433 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero |
| 434 | instantiation | 462, 465, 469, 538, 466, 470, 518*, 521* | ⊢  |
| | : , : , :  |
| 435 | instantiation | 574, 672, 684, 610, 463, 612, 613, 519, 523 | ⊢  |
| | : , : , : , : , : , :  |
| 436 | instantiation | 591, 610, 684, 612, 463, 519, 523 | ⊢  |
| | : , : , : , :  |
| 437 | instantiation | 615, 464 | ⊢  |
| | : , : , :  |
| 438 | instantiation | 586, 613, 465, 466, 467* | ⊢  |
| | : , :  |
| 439 | instantiation | 615, 468 | ⊢  |
| | : , : , :  |
| 440 | instantiation | 586, 613, 469, 470, 471* | ⊢  |
| | : , :  |
| 441 | instantiation | 682, 668, 472 | ⊢  |
| | : , : , :  |
| 442 | instantiation | 579, 473, 581 | , ⊢  |
| | : , :  |
| 443 | instantiation | 574, 610, 684, 672, 612, 474, 580, 505, 581 | , ⊢  |
| | : , : , : , : , : , :  |
| 444 | instantiation | 568 | ⊢  |
| | : , : , :  |
| 445 | instantiation | 475, 678, 649 | ⊢  |
| | : , :  |
| 446 | instantiation | 662, 649 | ⊢  |
| | :  |
| 447 | instantiation | 476, 525 | ⊢  |
| | :  |
| 448 | instantiation | 624 | ⊢  |
| | : , :  |
| 449 | instantiation | 477, 613, 644, 478 | ⊢  |
| | : , : , :  |
| 450 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 451 | instantiation | 579, 546, 479 | ⊢  |
| | : , :  |
| 452 | instantiation | 601, 480, 481 | ⊢  |
| | : , : , :  |
| 453 | conjecture | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
| 454 | instantiation | 482, 681, 484, 485, 486 | ⊢  |
| | : , : , :  |
| 455 | instantiation | 483, 681, 484, 485, 486, 487, 488, 489 | , ⊢  |
| | : , : , : , :  |
| 456 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod |
| 457 | instantiation | 540, 490, 491 | , ⊢  |
| | : , :  |
| 458 | conjecture | | ⊢  |
| | proveit.numbers.division.div_complex_closure |
| 459 | instantiation | 492, 571, 627 | ⊢  |
| | : , :  |
| 460 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 461 | instantiation | 493, 644, 494, 495 | ⊢  |
| | : , : , :  |
| 462 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.real_power_of_product |
| 463 | instantiation | 624 | ⊢  |
| | : , :  |
| 464 | instantiation | 615, 496 | ⊢  |
| | : , : , :  |
| 465 | instantiation | 497, 644 | ⊢  |
| | :  |
| 466 | instantiation | 501, 654, 498 | ⊢  |
| | : , :  |
| 467 | instantiation | 601, 499, 500 | ⊢  |
| | : , : , :  |
| 468 | instantiation | 615, 570 | ⊢  |
| | : , : , :  |
| 469 | instantiation | 540, 644, 571 | ⊢  |
| | : , :  |
| 470 | instantiation | 501, 654, 502 | ⊢  |
| | : , :  |
| 471 | instantiation | 601, 503, 504 | ⊢  |
| | : , : , :  |
| 472 | instantiation | 682, 677, 634 | ⊢  |
| | : , : , :  |
| 473 | instantiation | 579, 580, 505 | , ⊢  |
| | : , :  |
| 474 | instantiation | 624 | ⊢  |
| | : , :  |
| 475 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_int_closure_bin |
| 476 | conjecture | | ⊢  |
| | proveit.numbers.negation.mult_neg_one_left |
| 477 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.subtract_from_add |
| 478 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 479 | instantiation | 543, 506, 507 | ⊢  |
| | : , : , :  |
| 480 | instantiation | 574, 672, 547, 610, 508, 612, 546, 580, 581, 525 | ⊢  |
| | : , : , : , : , : , :  |
| 481 | instantiation | 574, 610, 684, 547, 612, 548, 508, 644, 567, 580, 581, 525 | ⊢  |
| | : , : , : , : , : , :  |
| 482 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space |
| 483 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space |
| 484 | instantiation | 624 | ⊢  |
| | : , :  |
| 485 | instantiation | 509, 681 | ⊢  |
| | :  |
| 486 | instantiation | 509, 510 | ⊢  |
| | :  |
| 487 | instantiation | 624 | ⊢  |
| | : , :  |
| 488 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.ket_one_in_qubit_space |
| 489 | instantiation | 511, 671, 622 | , ⊢  |
| | : , :  |
| 490 | instantiation | 682, 655, 512 | ⊢  |
| | : , : , :  |
| 491 | instantiation | 543, 513, 514 | , ⊢  |
| | : , : , :  |
| 492 | conjecture | | ⊢  |
| | proveit.numbers.addition.commutation |
| 493 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.product_of_pos_powers |
| 494 | instantiation | 682, 515, 665 | ⊢  |
| | : , : , :  |
| 495 | instantiation | 682, 515, 619 | ⊢  |
| | : , : , :  |
| 496 | instantiation | 601, 516, 517 | ⊢  |
| | : , : , :  |
| 497 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.sqrt_complex_closure |
| 498 | instantiation | 682, 520, 665 | ⊢  |
| | : , : , :  |
| 499 | instantiation | 615, 518 | ⊢  |
| | : , : , :  |
| 500 | instantiation | 522, 519 | ⊢  |
| | :  |
| 501 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_rational_non_zero__not_zero |
| 502 | instantiation | 682, 520, 619 | ⊢  |
| | : , : , :  |
| 503 | instantiation | 615, 521 | ⊢  |
| | : , : , :  |
| 504 | instantiation | 522, 523 | ⊢  |
| | :  |
| 505 | instantiation | 540, 644, 524 | , ⊢  |
| | : , :  |
| 506 | instantiation | 579, 564, 525 | ⊢  |
| | : , :  |
| 507 | instantiation | 574, 610, 684, 672, 612, 565, 580, 581, 525 | ⊢  |
| | : , : , : , : , : , :  |
| 508 | instantiation | 568 | ⊢  |
| | : , : , :  |
| 509 | conjecture | | ⊢  |
| | proveit.linear_algebra.complex_vec_set_is_vec_space |
| 510 | instantiation | 526, 684, 661 | ⊢  |
| | : , :  |
| 511 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.num_ket_in_register_space |
| 512 | instantiation | 682, 596, 527 | ⊢  |
| | : , : , :  |
| 513 | instantiation | 579, 546, 528 | , ⊢  |
| | : , :  |
| 514 | instantiation | 601, 529, 530 | , ⊢  |
| | : , : , :  |
| 515 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
| 516 | instantiation | 601, 531, 532 | ⊢  |
| | : , : , :  |
| 517 | instantiation | 601, 533, 534 | ⊢  |
| | : , : , :  |
| 518 | instantiation | 537, 644, 640, 538, 587, 535* | ⊢  |
| | : , : , :  |
| 519 | instantiation | 540, 644, 536 | ⊢  |
| | : , :  |
| 520 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero |
| 521 | instantiation | 537, 644, 589, 538, 587, 539* | ⊢  |
| | : , : , :  |
| 522 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 523 | instantiation | 540, 644, 554 | ⊢  |
| | : , :  |
| 524 | instantiation | 590, 541 | , ⊢  |
| | :  |
| 525 | instantiation | 682, 655, 542 | ⊢  |
| | : , : , :  |
| 526 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_natpos_closure |
| 527 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.e_is_real_pos |
| 528 | instantiation | 543, 544, 545 | , ⊢  |
| | : , : , :  |
| 529 | instantiation | 574, 672, 547, 610, 549, 612, 546, 580, 581, 566 | , ⊢  |
| | : , : , : , : , : , :  |
| 530 | instantiation | 574, 610, 684, 547, 612, 548, 549, 644, 567, 580, 581, 566 | , ⊢  |
| | : , : , : , : , : , :  |
| 531 | instantiation | 615, 550 | ⊢  |
| | : , : , :  |
| 532 | instantiation | 615, 551 | ⊢  |
| | : , : , :  |
| 533 | instantiation | 552, 610, 684, 672, 612, 553, 571, 627, 554 | ⊢  |
| | : , : , : , : , : , :  |
| 534 | instantiation | 555, 571, 627, 556 | ⊢  |
| | : , : , :  |
| 535 | instantiation | 557, 627, 613, 614* | ⊢  |
| | : , :  |
| 536 | instantiation | 682, 655, 558 | ⊢  |
| | : , : , :  |
| 537 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.real_power_of_real_power |
| 538 | instantiation | 682, 668, 559 | ⊢  |
| | : , : , :  |
| 539 | instantiation | 601, 560, 561 | ⊢  |
| | : , : , :  |
| 540 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_complex_closure |
| 541 | instantiation | 682, 655, 562 | , ⊢  |
| | : , : , :  |
| 542 | instantiation | 682, 668, 563 | ⊢  |
| | : , : , :  |
| 543 | theorem | | ⊢  |
| | proveit.logic.equality.sub_right_side_into |
| 544 | instantiation | 579, 564, 566 | , ⊢  |
| | : , :  |
| 545 | instantiation | 574, 610, 684, 672, 612, 565, 580, 581, 566 | , ⊢  |
| | : , : , : , : , : , :  |
| 546 | instantiation | 579, 644, 567 | ⊢  |
| | : , :  |
| 547 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 548 | instantiation | 624 | ⊢  |
| | : , :  |
| 549 | instantiation | 568 | ⊢  |
| | : , : , :  |
| 550 | instantiation | 586, 608, 644, 587, 569* | ⊢  |
| | : , :  |
| 551 | instantiation | 615, 570 | ⊢  |
| | : , : , :  |
| 552 | conjecture | | ⊢  |
| | proveit.numbers.addition.disassociation |
| 553 | instantiation | 624 | ⊢  |
| | : , :  |
| 554 | instantiation | 590, 571 | ⊢  |
| | :  |
| 555 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_triple_13 |
| 556 | instantiation | 572 | ⊢  |
| | :  |
| 557 | conjecture | | ⊢  |
| | proveit.numbers.negation.pos_times_neg |
| 558 | instantiation | 573, 640 | ⊢  |
| | :  |
| 559 | instantiation | 682, 677, 650 | ⊢  |
| | : , : , :  |
| 560 | instantiation | 574, 610, 684, 672, 612, 592, 627, 618, 575 | ⊢  |
| | : , : , : , : , : , :  |
| 561 | instantiation | 576, 684, 610, 592, 612, 627, 618, 613, 577* | ⊢  |
| | : , : , : , : , :  |
| 562 | instantiation | 682, 668, 578 | , ⊢  |
| | : , : , :  |
| 563 | instantiation | 682, 677, 649 | ⊢  |
| | : , : , :  |
| 564 | instantiation | 579, 580, 581 | ⊢  |
| | : , :  |
| 565 | instantiation | 624 | ⊢  |
| | : , :  |
| 566 | instantiation | 682, 655, 582 | , ⊢  |
| | : , : , :  |
| 567 | instantiation | 682, 655, 583 | ⊢  |
| | : , : , :  |
| 568 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 569 | instantiation | 601, 584, 585 | ⊢  |
| | : , : , :  |
| 570 | instantiation | 586, 618, 644, 587, 588* | ⊢  |
| | : , :  |
| 571 | instantiation | 682, 655, 589 | ⊢  |
| | : , : , :  |
| 572 | axiom | | ⊢  |
| | proveit.logic.equality.equals_reflexivity |
| 573 | conjecture | | ⊢  |
| | proveit.numbers.negation.real_closure |
| 574 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.disassociation |
| 575 | instantiation | 590, 613 | ⊢  |
| | :  |
| 576 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_neg_any |
| 577 | instantiation | 591, 684, 610, 592, 612, 627, 618 | ⊢  |
| | : , : , : , :  |
| 578 | instantiation | 682, 677, 593 | , ⊢  |
| | : , : , :  |
| 579 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure_bin |
| 580 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.i_is_complex |
| 581 | instantiation | 682, 655, 594 | ⊢  |
| | : , : , :  |
| 582 | instantiation | 682, 668, 595 | , ⊢  |
| | : , : , :  |
| 583 | instantiation | 682, 596, 597 | ⊢  |
| | : , : , :  |
| 584 | instantiation | 615, 616 | ⊢  |
| | : , : , :  |
| 585 | instantiation | 601, 598, 599 | ⊢  |
| | : , : , :  |
| 586 | conjecture | | ⊢  |
| | proveit.numbers.division.div_as_mult |
| 587 | instantiation | 600, 681 | ⊢  |
| | :  |
| 588 | instantiation | 601, 602, 603 | ⊢  |
| | : , : , :  |
| 589 | instantiation | 682, 668, 604 | ⊢  |
| | : , : , :  |
| 590 | conjecture | | ⊢  |
| | proveit.numbers.negation.complex_closure |
| 591 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.elim_one_any |
| 592 | instantiation | 624 | ⊢  |
| | : , :  |
| 593 | instantiation | 682, 605, 606 | , ⊢  |
| | : , : , :  |
| 594 | conjecture | | ⊢  |
| | proveit.physics.quantum.QPE._phase_is_real |
| 595 | instantiation | 682, 677, 607 | , ⊢  |
| | : , : , :  |
| 596 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real |
| 597 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
| 598 | instantiation | 617, 608, 627 | ⊢  |
| | : , :  |
| 599 | instantiation | 609, 672, 684, 610, 611, 612, 627, 618, 613, 614* | ⊢  |
| | : , : , : , : , : , :  |
| 600 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
| 601 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 602 | instantiation | 615, 616 | ⊢  |
| | : , : , :  |
| 603 | instantiation | 617, 618, 627 | ⊢  |
| | : , :  |
| 604 | instantiation | 682, 664, 619 | ⊢  |
| | : , : , :  |
| 605 | instantiation | 635, 620, 636 | ⊢  |
| | : , :  |
| 606 | assumption | | ⊢  |
| 607 | instantiation | 682, 621, 622 | , ⊢  |
| | : , : , :  |
| 608 | instantiation | 682, 655, 623 | ⊢  |
| | : , : , :  |
| 609 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 610 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 611 | instantiation | 624 | ⊢  |
| | : , :  |
| 612 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 613 | instantiation | 682, 655, 625 | ⊢  |
| | : , : , :  |
| 614 | instantiation | 626, 627 | ⊢  |
| | :  |
| 615 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 616 | instantiation | 628, 629, 679, 630* | ⊢  |
| | : , :  |
| 617 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.commutation |
| 618 | instantiation | 682, 655, 631 | ⊢  |
| | : , : , :  |
| 619 | instantiation | 632, 665, 633 | ⊢  |
| | : , :  |
| 620 | instantiation | 648, 634, 663 | ⊢  |
| | : , :  |
| 621 | instantiation | 635, 636, 637 | ⊢  |
| | : , :  |
| 622 | assumption | | ⊢  |
| 623 | instantiation | 645, 646, 638 | ⊢  |
| | : , : , :  |
| 624 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 625 | instantiation | 682, 668, 639 | ⊢  |
| | : , : , :  |
| 626 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.elim_one_right |
| 627 | instantiation | 682, 655, 640 | ⊢  |
| | : , : , :  |
| 628 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.neg_power_as_div |
| 629 | instantiation | 682, 641, 642 | ⊢  |
| | : , : , :  |
| 630 | instantiation | 643, 644 | ⊢  |
| | :  |
| 631 | instantiation | 645, 646, 671 | ⊢  |
| | : , : , :  |
| 632 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_rational_pos_closure_bin |
| 633 | instantiation | 682, 680, 671 | ⊢  |
| | : , : , :  |
| 634 | instantiation | 662, 647 | ⊢  |
| | :  |
| 635 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.int_interval_within_int |
| 636 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.zero_is_int |
| 637 | instantiation | 648, 649, 650 | ⊢  |
| | : , :  |
| 638 | instantiation | 651, 671, 679 | ⊢  |
| | : , :  |
| 639 | instantiation | 682, 677, 663 | ⊢  |
| | : , : , :  |
| 640 | instantiation | 682, 668, 652 | ⊢  |
| | : , : , :  |
| 641 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
| 642 | instantiation | 682, 653, 654 | ⊢  |
| | : , : , :  |
| 643 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
| 644 | instantiation | 682, 655, 656 | ⊢  |
| | : , : , :  |
| 645 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.unfold_subset_eq |
| 646 | instantiation | 657, 658 | ⊢  |
| | : , :  |
| 647 | instantiation | 682, 659, 671 | ⊢  |
| | : , : , :  |
| 648 | conjecture | | ⊢  |
| | proveit.numbers.addition.add_int_closure_bin |
| 649 | instantiation | 660, 678, 661 | ⊢  |
| | : , :  |
| 650 | instantiation | 662, 663 | ⊢  |
| | :  |
| 651 | conjecture | | ⊢  |
| | proveit.numbers.addition.add_nat_pos_closure_bin |
| 652 | instantiation | 682, 664, 665 | ⊢  |
| | : , : , :  |
| 653 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero |
| 654 | instantiation | 682, 666, 667 | ⊢  |
| | : , : , :  |
| 655 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 656 | instantiation | 682, 668, 669 | ⊢  |
| | : , : , :  |
| 657 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.relax_proper_subset |
| 658 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
| 659 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_pos_within_int |
| 660 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_int_closure |
| 661 | instantiation | 682, 670, 671 | ⊢  |
| | : , : , :  |
| 662 | conjecture | | ⊢  |
| | proveit.numbers.negation.int_closure |
| 663 | instantiation | 682, 683, 672 | ⊢  |
| | : , : , :  |
| 664 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
| 665 | instantiation | 673, 674, 675 | ⊢  |
| | : , :  |
| 666 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero |
| 667 | instantiation | 682, 676, 681 | ⊢  |
| | : , : , :  |
| 668 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 669 | instantiation | 682, 677, 678 | ⊢  |
| | : , : , :  |
| 670 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
| 671 | assumption | | ⊢  |
| 672 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 673 | conjecture | | ⊢  |
| | proveit.numbers.division.div_rational_pos_closure |
| 674 | instantiation | 682, 680, 679 | ⊢  |
| | : , : , :  |
| 675 | instantiation | 682, 680, 681 | ⊢  |
| | : , : , :  |
| 676 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int |
| 677 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 678 | instantiation | 682, 683, 684 | ⊢  |
| | : , : , :  |
| 679 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat1 |
| 680 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
| 681 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat2 |
| 682 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 683 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 684 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| *equality replacement requirements |